tg15∘⋅tg25∘⋅tg35∘⋅tg85∘tg15∘⋅tg25∘⋅tg35∘⋅tg85∘=?

tg15∘⋅tg25∘⋅tg35∘⋅tg85∘tg15∘⋅tg25∘⋅tg35∘⋅tg85∘=?

$\tan(15°)\cdot \tan(25°)\cdot \tan(35°)\cdot \tan(85°)=1$

$\tan(15°)\cdot \tan(25°)\cdot \tan(35°)\cdot \tan(85°)\times \tan(15°)\cdot \tan(25°)\cdot \tan(35°)\cdot \tan(85°) =1\times 1 = 1$

Could you expand on your answer please Heureka?

How do you know that that product is 1?

 I asssume you did not use a calculator ?

tan(15°) tan(25°) tan(35°) tan(85°) =(2 - sqrt(3)) tan((5 π)/36) tan((7 π)/36) cot(π/36)(Radians) =1